Download App

Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae4 Marks
Question
Prove that: $\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$
✓

Answer

We have, $\text{LHS}=\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}$ $=\ \frac{2\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}{2\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)}$ $=\ \frac{\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}{\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}$ $= \tan\Big(\frac{\text{A+B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$ $=\ \text{RHS}$ $\therefore\ \frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A+B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big).$ Hence proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Differentiate the following from first principle:$\frac{\text{x}^2+1}{\text{x}}$
→
In each of the followin find the equation of the hyperbola satisying the given conditions:

vertices $(0, \pm3)$, foci $(0, \pm5)$ [NCERT]

→
For any two sets of A and B, prove that:

$\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$

→
Find the derivative of the following functions: $3\cot\text{x} + 5\text{cosec}\text{x}$
→
If for non-zerox, $\text{af(x)}+\text{bf}\Big(\frac{1}{\text{x}}\Big)=\frac{1}{\text{x}}-5,$ where $\text{a}\neq\text{b},$ then find f(x).
→
Find the sum of the following series: 9 + 99 + 999 + ... to n terms.
→
Find the mean and variance of frequency distribution given below:
$x_i$ $1\leq\text{x}<3$ $3\leq\text{x}<5$ $5\leq\text{x}<7$ $7\leq\text{x}<10$
$f_1$ 6 4 5 1
→
Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3, -9) and (5, -8).
→
Solve the following systems of linear inequations graphically: $2\text{x}+3\text{y}\leq35,\text{y}\geq3,\text{x}\geq2,\text{x}\geq0,\text{y}\geq0$
→
Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axis.
→